Answers
Answer:
anticlockwise; reflection about x = 0; reflection about y = x - 1
Step-by-step explanation:
To get from A to A', we have to rotate anticlockwise. This rotation would take us around the coordinate plane from the first quadrant to the fourth quadrant to the third quadrant to the second quadrant. Clockwise about (0, -1) would not bring us to A'. To get from A' to A'', we to reflect across the line x = 0. As you can see in the image, the two triangles mirror each other across a vertical line in the center of them, and this vertical line would be x = 0 because both triangles are at least 1 unit away from it (they are equidistant from this line)
A single transformation that could map A onto A'' would be a reflection about y = x - 1. Both triangles happen to meet at this point so you might be able to visualize it. However, we can also test some points to see if this works. First, we can test the right-most point of A (which is the top-most point of A''). This point on A is (6, 0). If this point was reflected across y = x - 1, y would become 6 - 1 or 5, and since y = x - 1 is the same as x = y + 1, x would become 0 + 1 or 1. Indeed, the equivalent point on A'' is (1, 5).
Related Questions
A, B, and C are midpoints of ∆XYZ. What is the length of yz
Answers
Answer:
Step-by-step explanation:
Comment
When you join 2 consecutive midpoints with a line between them, the length of that line is 1/2 the length of the side opposite the line you just drew.
In other words 24 is 1/2 the length of yz.
Solution
1/2 yz = AB
AB = 24
1/2 yz = 24 Multiply both sides by 2
2(1/2 yz) = 2*24
yz = 48
Answer
yz = 48
3/8 TIMES 2/5 =
SIMPLIFIED
Answers
Answer:
3/20
decimal form: 0.15
explanation: yea
Which graphs do not show a constant rate of change? Check all that apply.
On a coordinate plane, a parabola opens down.
On a coordinate plane, a line has a negative slope.
On a coordinate plane, a horizontal line is graphed.
On a coordinate plane, a curve curves downwards.
Answers
Answer:
a horizontal line is graphed
Step-by-step explanation:
It does not change it will always stay at the same y but just different x.
The rate of change/slope is the change in y divided by a corresponding change in x.
Hi. . .
A n s w e r : -
A, and D.
E x p l a n a t i o n :Cause- A, and D do not show the constant rate of the change.
Hope It Helps . . .
Use the substitutions u= 1/x^2 and v= 1/y^2 to solve the system of equations. express numbers as integers or simplified fractions.
-5/x^2 + 1/y^2 =-16
13/x^2- 1/y^2 =48
Answers
Answer:
-5 u + 1 v = (-16)
12 u - 1v = 48
adding,
7 u = 32
u = 32/7V = (-16) + 5(32/7)
V = (-16) +160/7
V = -112 + 160/7
V = 48/7The sides of this rectangle are marked off in centimeters. If the rectangle is enlarged proportionally so that the longer side is 35 cm, how long will the shorter side be?
PLEASE I REALLY NEED HELP (the answer is not 10)
Answers
the length of the shorter side is:L = 13.125cm
how long will the shorter side be?
In the longer side we have 8 segments.
We know that the side measures 35 cm, then each one of the 8 segments measures:
35cm/8 = 4.375cm
Now, we can see that in the shorter side we have 3 of these segments.
Then the length of the shorter side is:
L = 3*(4.375cm) = 13.125cm
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What is the expression of g(x) when we perform the following sequence of transformations onto the parent function fx=|x|:
a) compress horizontally by a factor of 2
b) shift right 1 unit
c) shift up 3 units
Answers
The expression of function g(x) is [tex]|\frac {x - 1}2| + 3[/tex]
How to determine the expression?The function is given as:
[tex]f(x) = |x|[/tex]
When the function is compressed horizontally by a factor of 2, the rule is:
f'(x) = f(x/2)
So, we have:
[tex]f(x) = |\frac x2|[/tex]
When the function is shifted left by 1 unit, the rule is:
f"(x) = f(x + 1)
So, we have:
[tex]f'(x) = |\frac {x - 1}2|[/tex]
When the function is shifted up by 3 units, the rule is:
g(x) = f"(x) + 3
So, we have:
[tex]g(x) = |\frac {x - 1}2| + 3[/tex]
Hence, the expression of function g(x) is [tex]|\frac {x - 1}2| + 3[/tex]
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A bag has 20 cubes in it. 6 of the cubes are
green.
You take one cube out of the bag at random.
Which four values below show the probability
that you take out a cube that is green?
6
14
6%
0.3
30% 0.6
3 6
5 20
6
10
60%
3
10
0.03
6
26
Answers
Answer: 0.3, [tex]\frac{6}{20}[/tex], [tex]\frac{3}{10}[/tex], 30%
Step-by-step explanation:
We will divide wanted outcomes by possible outcomes.
[tex]\displaystyle \frac{\text{wanted outcomes, green cubes}}{\text{possible outcomes, cubes in bag}} =\frac{6}{20}[/tex]
Now, we will find four values equivalent to [tex]\frac{6}{20}[/tex]. See attached.
0.3,
30%,
3/10
6/20
Why? Well, see below!
The total number of cubes present in the bag is 20. 6 of these cubes present are green. Since 20 is the total number, that would mean that 100% = 20. Because 100 divided by 20 = 5, we can multiply 6 by 5 to get the amount of cubes that would be green out of 100.
6 x 5 = 30
Therefore, 30/100 cubes are green. This also is representative of the probability of taking a cube out that is green because it’s a ratio of 30 green cubes : 100 total cubes.
Because 30/100 is not a whole number, anything equivalent to 30/100 will be our answer. In decimated form, this converts to 0.3. In fraction form, these numbers both can be divided by 5 since they are even.
100 / 5 = 20
30 / 5 = 6
However, we are not done. 6/20 can also be reduced by 2.
20 / 2 = 10
6 / 2 = 3
Your final fraction conversion would be 3/10, which is an answer choice. Since 3/10 = 30/100, we know that as a percentage, that is the equivalent to 30%.
6/20 is also our answer because it is the same fraction as 3/10, it just is not reduced.
Your final answers: 30%, 3/10, 6/20, 0.3. If you need help, let me know and I will gladly assist you.
helppp pleaseee quick points
Answers
The required algebraic expression is Y = 3X + 2
This table describe the relation between x and y
x = 2 3 4 5
y = 8 11 14 17
What is algebraic expression?Alegebraic expression consists of constant and variable. eg x, y, z etc.
As the data given in the table, we conclude that:
1) The difference in the values of y is 3.
2) When we multiply this difference by x and add 2 it gives the next value of y.
so the from above discussion Y = 3X + 2
Thus, The required algebraic expression is Y = 3X + 2
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Find x. Round your answer to the nearest integer.
Answers
Answer:
B. 20
Step-by-step explanation:
Cos a = b/c
Cos 53° = b/25
b = 25 × 0,6 = 15
x = √(25² - 15²)
x = √(625 - 225)
x = √400
x = 20
I did 14a already. How do I do 14b?
y = 0.167x - 0.467
Answers
T probability of rolling doubles after 45 tosses is 0.156
How to determine the regression equation?To do this, we enter the data values in a graphing calculator.
From graphing calculator, we have the following summary:
Sum of X = 550Sum of Y = 87Mean X = 55Mean Y = 8.7Sum of squares (SSX) = 8250Sum of products (SP) = 1375The regression equation is
y = bx + a
Where
b = SP/SSX = 1375/8250 = 0.16667
a = MY - bMX = 8.7 - (0.17*55) = -0.46667
So, we have:
y = 0.16667x - 0.46667
Approximate
y = 0.167x - 0.467
When the number of tosses is 45, we have:
y = 0.167 * 45 - 0.467
Evaluate
y = 7.048
Approximate
y = 7
45 tosses gives 7 doubles.
So, the probability is:
P = 7/45
Evaluate
P = 0.156
Hence, the probability of rolling doubles after 45 tosses is 0.156
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look at the image.......
Answers
Answer:
A. The sloped graph doesn't represent the verbal description because the slope is 1 hot dog per 4 min
Step-by-step explanation:
B. Option b is valid response of the verbal description because the statements say Katie starts with 3 bonus hotdogs and then eats 4 hotdogs/min. This is the slope-int of the verbal description.
C. &D. When you substitute the table values of x into the slope-int equation, you should get the y-values listed in the table
Hope it helps!
Think of 5 positive integers that have a mode of 2 and 5, a median of 5 and a mean of 5.
Answers
Answer:
S = {2, 2, 5, 5, 11}
Step-by-step explanation:
So you can partially build a data set given this information. There is going to be 5 positive numbers and the median is going to be 5 so the data set is going to have 5 in the middle which should look like this
S = {a, b, 5, c, d} where a, b, c, d are the other values. Since it has a mode of 2 and 5 that means that the occurrences of 2 and 5 will be equal, otherwise it would only have 1 mode. and they have to appear at least twice since if they only appeared once, there would either be another mode, or the data set would have 5 modes.
So the data set is going to look like this
S = {2, 2, 5, 5, d}
Now the only thing left to do is calculate d. This is where you use the mean to determine the last value. The mean can be calculated as
(the sum of the data set) / (the amount of values in the data set)
Since we know the mean you can set up an equation to find the value of d
[tex]5 = \frac{2+2+5+5+d}{5}\\5=\frac{14+d}{5}\\25=14+d\\11=d[/tex]
so the last value is 11. This gives you the complete data set of 5 positive integers
S = {2, 2, 5, 5, 11}
Can someone please help me solve this question? Pls provide a step by step explanation too… Ty!
Answers
Answer:B 1/2
I can't type math symbols well in BRAINLY, so I use pictures╯﹏╰
= (x^2-9)/(4x-12) • 2/(x+3)
= (x-3)(x+3)/4(x-3) • 2/(x+3)
= 2/4
= 1/2
Then
The correct answer is B.
Type the correct answer in each box. A circle is centered at the point (5, -4) and passes through the point (-3, 2).
The equation of this circle is (x + )2 + (y + )2 =
Answers
Answer:
[tex](x-5)^2+(y+4)^2=100[/tex]
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven:
center = (5, -4)point on circle = (-3, 2)Substitute the given values into the circle equation and solve for r:
[tex]\implies r^2=(-3-5)^2+(2-(-4))^2[/tex]
[tex]\implies r^2=(-8)^2+(6)^2[/tex]
[tex]\implies r^2=64+36[/tex]
[tex]\implies r^2=100[/tex]
[tex]\implies r=\sqrt{100}[/tex]
[tex]\implies r=10[/tex]
Substitute the given center and the found value of r into the circle equation to create the equation of the circle:
[tex]\implies (x-5)^2+(y-(-4))^2=10^2[/tex]
[tex]\implies (x-5)^2+(y+4)^2=100[/tex]
Find the value of x for which ABCD must be a parallelogram.
1
7
14
28
Note:This better be worth my 27 points
Answers
Answer:
A. 1
Step-by-step explanation:
18-4x=7x+7
Use this equation to find x.
Simplify.
18-4x=7x+7
Subtract 7 from both sides.
11-4x=7x
Add 4x to both sides.
11=11x
Divide 11 from both sides.
x=1
Hope this helps!
m and n are both prime numbers. Find the values of m and n so that 2704× m/n is a perfect cube.
Answers
Since 2704 = 2⁴ × 13², we need [tex]m = 13[/tex] and [tex]n=2[/tex], since this gives
[tex]\dfrac{2704m}n = \dfrac{2^4 \times 13^2 \times 13}2 = 2^3 \times 13^3 = 26^3[/tex]
The values of m and n that make 2704 × m/n a perfect cube are:
m = 13 and n = 2.
We have,
We can start by factoring 2704, which is 52².
So we have:
= 2704 × m/n
= 52² × m/n
= (2² × 13²) × m/n
For the expression to be a perfect cube, we need all the prime factors to appear in groups of three.
Since 2 and 13 appear only once each, we need to find another factor that appears twice.
Since m and n are both prime, and the fraction m/n is simplified, there are only two possible values for m and n:
m = 2 and n = 13, or
m = 13 and n = 2
Let's try the first case:
2704 × m/n = 2704 × 2/13 = 416
416 is not a perfect cube, so this case does not work.
Now let's try the second case:
2704 × m/n = 2704 × 13/2 = 17696
17696 is 28³, which is a perfect cube.
Therefore,
The values of m and n that make 2704 × m/n a perfect cube are:
m = 13 and n = 2.
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Question content area top Part 1 Three friends all live on the same street that runs west to east. lives blocks from . lives from . If the street is represented by a number line and 's house is located at 0, what are the possible locations for 's house?
Answers
Based on the information, it can be inferred that Carl's house is 6 blocks from Ann's house.
How to identify where each friend's house is?To identify where each friend's house is, we must graph the information provided as shown below.
Once we have made the graph we will identify that Carl's house is 6 blocks east of Ann's house.
Note: This question is incomplete because there is some information missing. Here is the missing information:
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9
Which system of Inequalities is represented by the graph?
Answers
The inequality equation of the lines are given as x + 2y ≤ 5 and 3x + y ≤ 4. Then the correct option is C.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The graph is given below.
From the graph, equation of the lines are given as
x + 2y = 5 and 3x + y = 4
But for the inequality is shown in the graph. Then the inequality equation of the lines are given as
x + 2y ≤ 5 and 3x + y ≤ 4
Then the correct option is C.
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Work out the rule for the nth term then work out the 100 term
th
a) 3, 5, 7, 9, 11, 13....
b) 12, 20, 28, 36, 44....
c) 19, 29, 39, 49, 59....
d) 7, 10, 13, 16, 19....
e) 14, 20, 26, 32, 38....
f) 55, 60, 65, 70, 75...
g) 8, 17, 26, 35, 44....
Answers
3. The number which when substituted in a polynomial makes its value zero.
Answers
The number which when substituted in a polynomial makes its value zero is called the zero of the polynomial.
What is zero of a polynomial?The zero of a polynomial can be defined as the points where the polynomial becomes zero as a whole.
In other words, The zeros of a polynomial p(x) are the values of x which satisfy the equation p(x) = 0
For example, the zero of the polynomial f(x) = x³- 12x²+ 20x is x = 0 or x = 10 or x = 2.
This is because f(x) = o when we substitute those x values.
Therefore, the number which when substituted in a polynomial makes its value zero is called the zero of the polynomial.
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Calculate the value of x.
Answers
Answer:
x = 17deg
Step-by-step explanation:
Let angle y be the unknown angle IN THE TRIANGLE.
Angle y = 180 - 90 - 73
= 17deg
Angle x = Angle y (Alternate angles on 2 parallel lines)
Angle x = 17 deg
Answer:
17° is the answer.
Prove experimentally that an exterior angle is formed by producing a side of a triangle equals to the sum of non adjacent interior angle. .
Answers
It is proved in the answer that an exterior angle of the triangle equals the sum of two opposite interior angles.
What is the exterior angle property of a triangle?If a triangle's side is created, the outside angle that results is equal to the product of the two opposite internal angles.
In the figure given below we can see:
∠BCD is the exterior angle of the triangle
∠ABC + ∠BAC + ∠BCA = 180° (Angle sum property of a triangle)
∠BCA + ∠BCD = 180°(Linear pair)
From both equations we can say that:
∠ABC + ∠BAC + ∠BCA = ∠BCA + ∠BCD
∠ABC + ∠BAC = ∠BCD
Hence Proved
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In the first half of a basketball game, a player scored 9 points on free throws and then scored a number of 2-port
shots. In he second half, he player scored the same number of 3-point shots as the number of 2 point slots scored n
the first half. Which expression represents the total number of points the player scored in the game?
O 2r + 3r + 9
© 2r + 3 + 9
O 2r + 3r + 9x
© 2 + 3r + 9
Save
Answers
Answer: I thin The first one 2r+3r+9
Step-by-step explanation: Because he scored a number of 2 port shots which means he scored more than one but the 9 points is just 9 points from free throws which gives only 1 point each and 3 port shots and much as 2 point shots so 3r also
2r+3r+ just 9
explain please thanks
Answers
Answer:
26542%
Step-by-step explanation:
12,209,400/46,000 = 265.421
265.421 × 100 ≈ 26542%
The angle between the lines joining the origin to the points of intersection of the straight line y = 3x + 2 with the curve x² + 2xy + 3y² + 4x + 8y - 11 = 0 is?
Answers
The angle between the lines joining the origin to the points of intersection of the degenerated elipse and the straight line is approximately 136.635°.
What is the measure of a triangle?
We have the graphs of a degenerated ellipse and a line, which intercept each other at points (x₁, y₁) = (-0.293, 1.121) and (x₂, y₂) = (- 1.707, - 3.121). A representation of the situation is shown in the image attached below.
Now we find the angle between the two lines by dot product:
[tex]\cos \theta = \frac{(- 0.293, 1.121)\,\bullet \,(- 1.707, - 3.121)}{1.159 \,\cdot\, 3.557}[/tex]
[tex]\cos \theta = - 0.727[/tex]
θ ≈ 136.635°
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Question 3(Multiple Choice Worth 1 points) (08.03 LC) A box plot is shown below: A box and whisker plot is shown using a number line from 20 to 45 with primary markings and labels at 20, 25, 30, 35, 40, 45. In between two primary markings are 4 secondary markings. The box extends from 26 to 38 on the number line. A line in the box is at 31. The whiskers end at 20 and 43. The title of the art is Visitors at the Exhibition, and below the line is written Number of Visitors. What is the median and Q1 of the data set represented on the plot? Median = 31; Q1 = 26 Median = 30; Q1 = 26 Median = 31; Q1 = 20 Median = 30; Q1 = 20
Answers
The median in the box plot is: 31
Q1 (lower quartile) = 26
What is the Median and Q1 of a a Data in a Box Plot?The median is the value at the vertical line that divides the box.
The Q1 (lower quartile) is the value at the beginning of the edge of the box.
Thus, from the given box plot, we have the following:
Median = 31
Q1 (lower quartile) = 26
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Allen is horrible at managing his money. For example, he
recently invested $100,000-part of it in a company that
makes "fish-flavored" chicken and the rest in a company
that makes spray-on vitamins. Somehow he managed to earn
a 3% profit on the fish-flavored chicken investment and 1%
profit on the spray-on vitamin deal. If Allen made a profit
of $2,600 from both investments, how much did he invest in
the fish-flavored chicken company?
Answers
Answer:
$80,000
Step-by-step explanation:
Define the variables:
Let x = "fish-flavored" chicken company investment (in dollars)
Let y = spray-on vitamins company investment (in dollars)
If Allen invested a total of $100,000:
⇒ x + y = 100000
Given:
3% profit on "fish-flavored" chicken investment 1% profit on pray-on vitamins investmentTotal profit = $2,600⇒ 0.03x + 0.01y = 2600
Rewrite the first equation to make y the subject:
⇒ y = 100000 - x
Substitute into the second equation and solve for x:
⇒ 0.03x + 0.01(100000 - x) = 2600
⇒ 0.03x + 1000 - 0.01x = 2600
⇒ 0.02x + 1000 = 2600
⇒ 0.02x = 1600
⇒ x = 80000
Therefore, Allen invested $80,000 in the "fish-flavored" chicken company.
A sports club rewards teams based on overall points earned in a season. The data for points are shown in the table, where Low represents the fewest points scored and High represents the highest points scored by a single team member.
Team Low High Range Mean Median IQR σ
Team L 4 17 13 9.4 9 9.75 4.8
Team M 6 14 8 9.7 9.5 6.25 3.2
Team N 1 20 19 13 14.5 4.75 5.6
Part A: If the club wants to award the team that has the most consistent scoring among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)
Part B: If the club wants to award the team with the highest average score, which team should it choose and why? Justify your answer mathematically.
Answers
Answer:
PART A:
The range, the IQR (inter-quartile range) and the standard deviations are measures which are used to measure the spread of a data set.
A dataset is more consistent relative to another data set when the standard deviation is less than that of the other data set.
From the table, it can be seen that Team C has the least standard deviation.
Therefore, If the club wants to award the team that has the most consistent scoring among its team members, team C should be chosen.
PART B
The mean and the median is a measure of center of a data set.
The mean describes the average of a data set.
From the table, it can be seen that Team B has the highest average score.
Therefore, If the club wants to award the team with the highest average score, team B should be chosen.
-8
-4
8
-4
y
-8
y = -x + 5
4
80
x
What is the solution of the system of equations?
Answers
The solution of the equation is 5477x + 12y = -56
How to determine the solutionGiven the equation;
-8 -48-4y-8y = -x + 5480x
First, we collect like terms
-56 - 12y = 5477x
Collect the numbers with variables together
-56 = 5477x + 12y
Thus, the solution of the equation is 5477x + 12y = -56
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A general formula for a parabola is y2=4px. what is the value of p in the equation y2=−4x?
Answers
The value of p is -1 in the given equation of of parabola.
What is a parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point called focus and a line called the directrix.
Equation for a Parabola
The general formula or the equation for representing a parabola is given by,
y² = 4px
Here, (h,k) being the vertex of the parabola,
y = a(x-h)² + k
x = b(y-k)² + h
The focus of this parabola is given by (p, 0).
The directrix of the parabola is the line drawn perpendicular to the y-axis and traversing the point (-p, 0). The directrix is parallel to the parabola's axis.
What is the value of p in the equation for parabola?
The given equation is,
y² = -4x
Comparing this equation with the general formula of the parabola, we get,
p = -1
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